Quantifiers in Natural Language: Efficient Communication and Degrees of Semantic Universals

Recursive Numeral Systems Optimize the Trade-off Between Lexicon Size and Average Morphosyntactic Complexity

Human languages vary in terms of which meanings they lexicalize, but this variation is constrained. It has been argued that languages are under two competing pressures: the pressure to be simple (e.g., to have a small lexicon) and to allow for informative (i.e., precise) communication, and that which meanings get lexicalized may be explained by languages finding a good way to trade off between these two pressures. However, in certain semantic domains, languages can reach very high levels of informativeness even if they lexicalize very few meanings in that domain. This is due to productive morphosyntax and compositional semantics, which may allow for construction of meanings which are not lexicalized. Consider the semantic domain of natural numbers: many languages lexicalize few natural number meanings as monomorphemic expressions, but can precisely convey very many natural number meanings using morphosyntactically complex numerals. In such semantic domains, lexicon size is not in direct competition with informativeness. What explains which meanings are lexicalized in such semantic domains? We will propose that in such cases, languages need to solve a different kind of trade-off problem: the trade-off between the pressure to lexicalize as few meanings as possible (i.e, to minimize lexicon size) and the pressure to produce as morphosyntactically simple utterances as possible (i.e, to minimize average morphosyntactic complexity of utterances). To support this claim, we will present a case study of 128 natural languages' numeral systems, and show computationally that they achieve a near-optimal trade-off between lexicon size and average morphosyntactic complexity of numerals. This study in conjunction with previous work on communicative efficiency suggests that languages' lexicons are shaped by a trade-off between not two but three pressures: be simple, be informative, and minimize average morphosyntactic complexity of utterances.

Quantifiers satisfying semantic universals have shorter minimal description length

Despite wide variation among natural languages, there are linguistic properties thought to be universal to all or nearly all languages. Here, we consider universals at the semantic level, in the domain of quantifiers, which are given by the properties of monotonicity, quantity, and conservativity, and we investigate whether these universals might be explained by differences in complexity. First, we use a minimal pair methodology and compare the complexities of individual quantifiers using approximate Kolmogorov complexity. Second, we use a simple yet expressive grammar to generate a large collection of quantifiers and we investigate their complexities at an aggregate level in terms of both their minimal description lengths and their approximate Kolmogorov complexities. For minimal description length we find that quantifiers satisfying semantic universals are simpler: they have a shorter minimal description length. For approximate Kolmogorov complexity we find that monotone quantifiers have a lower Kolmogorov complexity than non-monotone quantifiers and for quantity and conservativity we find that approximate Kolmogorov complexity does not scale robustly. These results suggest that the simplicity of quantifier meanings, in terms of their minimal description length, partially explains the presence of semantic universals in the domain of quantifiers.

When do languages use the same word for different meanings? The Goldilocks principle in colexification

Lexical ambiguity is pervasive in language, and often systematic. For instance, the Spanish word dedo can refer to a toe or a finger, that is, these two meanings colexify in Spanish; and they do so as well in over one hundred other languages. Previous work shows that related meanings are more likely to colexify. This is attributed to cognitive pressure towards simplicity in language, as it makes lexicons easier to learn and use. The present study examines the interplay between this pressure and the competing pressure for languages to support accurate information transfer. We hypothesize that colexification follows a Goldilocks principle that balances the two pressures: meanings are more likely to attach to the same word when they are related to an optimal degree-neither too much, nor too little. We find support for this principle in data from over 1200 languages and 1400 meanings. Our results thus suggest that universal forces shape the lexicons of natural languages. More broadly, they contribute to the growing body of evidence suggesting that languages evolve to strike a balance between competing functional and cognitive pressures.

Indefinite Pronouns Optimize the Simplicity/Informativeness Trade-Off

The vocabulary of human languages has been argued to support efficient communication by optimizing the trade‐off between simplicity and informativeness. The argument has been originally based on cross‐linguistic analyses of vocabulary in semantic domains of content words, such as kinship, color, and number terms. The present work applies this analysis to a category of function words: indefinite pronouns (e.g., someone, anyone, no one). We build on previous work to establish the meaning space and featural make‐up for indefinite pronouns, and show that indefinite pronoun systems across languages optimize the simplicity/informativeness trade‐off. This demonstrates that pressures for efficient communication shape both content and function word categories. In doing so, our work aligns with several concurrent studies exploring the simplicity/informativeness trade‐off in functional vocabulary. Importantly, we further argue that the trade‐off may explain some of the universal properties of indefinite pronouns, thus reducing the explanatory load for linguistic theories.